A306008 - OEIS

%I #5 Jun 18 2018 08:58:49

%S 1,0,1,1,2,3,7,10,21,39,78

%N Number of non-isomorphic intersecting set-systems of weight n with no singletons.

%C An intersecting set-system is a finite set of finite nonempty sets (edges), any two of which have a nonempty intersection. The weight of a set-system is the sum of cardinalities of its elements. Weight is generally not the same as number of vertices.

%e Non-isomorphic representatives of the a(6) = 7 set-systems:

%e {{1,2,3,4,5,6}}

%e {{1,5},{2,3,4,5}}

%e {{3,4},{1,2,3,4}}

%e {{1,2,5},{3,4,5}}

%e {{1,3,4},{2,3,4}}

%e {{1,2},{1,3},{2,3}}

%e {{1,4},{2,4},{3,4}}

%Y Cf. A007716, A034691, A048143, A049311, A116540, A283877, A293606, A293607, A304867, A305999, A305854-A305857, A306005-A306007.

%K nonn,more

%O 0,5

%A _Gus Wiseman_, Jun 16 2018